Metallic structure on Lagrangian manifold
In this paper, the author convention with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying metallic structure F2 − αF − βI = 0. The horizontal subspace TH(E) is applied on the same structure. Next, some theorems are proved and obtained conditions under which the distribution L and M are ∇-parallel, ¯∇ anti half parallel when ∇ = ¯∇. Lastly, certain theorems on geodesics on the Lagrange manifold are deduced.
Keywords: Metallic structure; Lagrangian manifold; vertical space.
Received March 20, 2021
Accepted June 12, 2021
Published August 16, 2021
cited by : Journal of The Tensor Society (J.T.S.) Vol. 14 (2020), page 09 – 18.